std::function as a (non) const input parameter sent by & - c++

Question

I wonder why std::function<...(...)> & needs to be specified as const when passed as an input parameter to a function. AFAIK there is no way to change it, right? Here is an example that compiles and runs fine. If I remove the const qualifier I get an error:
#include <iostream>
#include <functional>
//int foo(std::function<int(int)> &f)
int foo(const std::function<int(int)> &f)
{
return f(6);
}
int main(int argc, char **argv)
{
auto f1 = [=](int i){ if (i<5) {return 8*2;} else {return 2;} };
auto f2 = [=](int i){ if (i>3) {return i*i;} else {return 2;} };
std::cout << foo(f1) << "\n";
}
When I use the declaration without the const I get the following error:
main.cpp: In function ‘int main(int, char**)’:
main.cpp:13:21: error: cannot bind non-const lvalue reference of type ‘std::function<int(int)>&’ to an rvalue of type ‘std::function<int(int)>’
std::cout << foo(f1) << "\n";
^
In file included from /usr/include/c++/7/functional:58:0,
from main.cpp:2:
/usr/include/c++/7/bits/std_function.h:685:7: note: after user-defined conversion: std::function<_Res(_ArgTypes ...)>::function(_Functor) [with _Functor = main(int, char**)::<lambda(int)>; <template-parameter-2-2> = void; <template-parameter-2-3> = void; _Res = int; _ArgTypes = {int}]
function<_Res(_ArgTypes...)>::
^~~~~~~~~~~~~~~~~~~~~~~~~~~~
main.cpp:4:5: note: initializing argument 1 of ‘int foo(std::function<int(int)>&)’
int foo(std::function<int(int)> &f)
^~~

Answer 1

A lambda is not a std::function, but a std::function can be created from a lambda. When you pass either f1 or f2 to foo(), the compiler must construct a temporary std::function object to give to the f parameter. However, an lvalue reference to a non-const object cannot be bound to a temporary object, exactly as the error message says.
To allow the passing of a temporary object, the f parameter must be changed to take the std::function by either:
value
lvalue reference to a const object
rvalue reference
Otherwise, you have to construct the std::function yourself in a variable, then pass that instead:
#include <iostream>
#include <functional>
//int foo(const std::function<int(int)> &f)
int foo(std::function<int(int)> &f)
{
return f(6);
}
int main(int argc, char **argv)
{
auto f1 = [=](int i){ if (i<5) {return 8*2;} else {return 2;} };
auto f2 = [=](int i){ if (i>3) {return i*i;} else {return 2;} };
std::function<int(int)> f = f1;
std::cout << foo(f) << "\n";
}